The locus of a point whose distance from... - Solved

Question 21

Mathematics Basic Geometry Easy

The locus of a point whose distance from \( (a, 0) \) is equal to its distance from \( y \) -axis, is

(A) \( y^{2}-2 a x+a^{2}=0 \)

(B) \( y-2 a x+a^{2}=0 \)

(C) \( \mathrm{y}^{2}+2 \mathrm{ax}+\mathrm{a}^{2}=0 \)

(D) \( y^{2}-2 a x+a=0 \)

✓ Correct Answer: Option A Verified Solution

Let the point be \((x, y)\). Its distance from the y-axis is \(|x|\).

\(\sqrt{(x-a)^2 + y^2} = |x|\)

\(x^2 - 2ax + a^2 + y^2 = x^2 \Rightarrow y^2 - 2ax + a^2 = 0\)

(This is a parabola with focus (a, 0) and the y-axis as its directrix.)

Answer: (A)

Full-Length Test Series

Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.